class Solution {
public:
    int integerBreak(int n) {
        if (n == 0 || n == 1) return 0;
        if (n == 2) return 1;
        vector<int> dp(n + 1);
        dp[0] = 0, dp[1] = 0, dp[2] = 1;
        for (int i = 3; i <= n; i++) {
            for (int j = 1; j <= i / 2; j++) {
                dp[i] = max(dp[i], j * (i - j));
                dp[i] = max(dp[i], j * dp[i - j]);
            }
        }
        return dp[n];
    }
};
